Superposition of diffusions with linear generator and its multifractal limit process
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 23-88.

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance and validation of the proposed model are demonstrated by real data of Internet traffic.

DOI : 10.1051/ps:2003008
Classification : 62M10, 60J60, 60G10, 93E12
Mots-clés : fractals, long range dependence, self-similarity, stationarity, higher order statistics, bispectrum, network traffic, superposition, diffusion processes, CIR process, DLG process, square root process 
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     title = {Superposition of diffusions with linear generator and its multifractal limit process},
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     publisher = {EDP-Sciences},
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     mrnumber = {1956073},
     zbl = {1017.60087},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps:2003008/}
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Iglói, End; Terdik, György. Superposition of diffusions with linear generator and its multifractal limit process. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 23-88. doi : 10.1051/ps:2003008. https://www.numdam.org/articles/10.1051/ps:2003008/
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  • Yoshioka, Hidekazu; Yoshioka, Yumi Risk assessment of river water quality using long-memory processes subject to divergence or Wasserstein uncertainty, Stochastic Environmental Research and Risk Assessment, Volume 38 (2024) no. 8, p. 3007 | DOI:10.1007/s00477-024-02726-y
  • Millan, G.; Chait, M.; Lefranc, G., 2016 IEEE International Conference on Automatica (ICA-ACCA) (2016), p. 1 | DOI:10.1109/ica-acca.2016.7778429
  • Grahovac, Danijel; Leonenko, Nikolai N.; Sikorskii, Alla; Tešnjak, Irena Intermittency of Superpositions of Ornstein–Uhlenbeck Type Processes, Journal of Statistical Physics, Volume 165 (2016) no. 2, p. 390 | DOI:10.1007/s10955-016-1616-7
  • Millán, G.; Lefranc, G. A Fast Multifractal Model for Self-Similar Traffic Flows in High-Speed Computer Networks, Procedia Computer Science, Volume 17 (2013), p. 420 | DOI:10.1016/j.procs.2013.05.054
  • Terdik, György Long Range Dependence in Third Order for Non-Gaussian Time Series, Advances in Directional and Linear Statistics (2011), p. 281 | DOI:10.1007/978-3-7908-2628-9_18
  • Terdik, G.; Gyires, T. LÉvy Flights and Fractal Modeling of Internet Traffic, IEEE/ACM Transactions on Networking, Volume 17 (2009) no. 1, p. 120 | DOI:10.1109/tnet.2008.925630
  • Tsolaki, Eleni P. Testing nonstationary time series for Gaussianity and linearity using the evolutionary bispectrum: An application to internet traffic data, Signal Processing, Volume 88 (2008) no. 6, p. 1355 | DOI:10.1016/j.sigpro.2007.12.011
  • Anh, V.V.; Leonenko, N.N. Log-normal, log-gamma and log-negative inverted gamma scenarios in multifractal products of stochastic processes, Statistics Probability Letters, Volume 78 (2008) no. 11, p. 1274 | DOI:10.1016/j.spl.2007.11.019
  • Anh, V.V.; Leonenko, N.N.; Sakhno, L.M. Statistical inference using higher-order information, Journal of Multivariate Analysis, Volume 98 (2007) no. 4, p. 706 | DOI:10.1016/j.jmva.2006.09.009
  • Rao, Tata Subba; Terdik, Gyorgy Multivariate Non-Linear Regression with Applications, Dependence in Probability and Statistics, Volume 187 (2006), p. 431 | DOI:10.1007/0-387-36062-x_19
  • Iglói, Endre Renormalization group of and convergence to the LISDLG process, ESAIM: Probability and Statistics, Volume 8 (2004), p. 102 | DOI:10.1051/ps:2004006
  • Gal, Z.; Terdik, G.; Igloi, E., 2001 IEEE Workshop on High Performance Switching and Routing (IEEE Cat. No.01TH8552) (2001), p. 197 | DOI:10.1109/hpsr.2001.923631

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